Scientific reasoning based on the biology of HIV justifies the use of Poison statistics as the approximate probability distribution underlying infection by HIV in chimpanzees trials. A statistic S using Bayesian predictive probabilities was used to generate P-values for assessing the statistical significance of various HIV trials in chimpanzees in frequentist Monte Carlo simulations. The P-values then quantified trial conclusions about vaccine efficacies. Actual titration and test strategies were used in computer simulation to assess conclusions from real trials.Major Findings: The computer simulations showed that in hypothetical repetitions of some (but certainly not all) actual trials, the values S produced in simulation were smaller than the corresponding actual trial value S[0] in fewer than 0.05 of the computer runs, indicating statistical significance under the usual frequentist criterion. Significance at the 0.05 level in many trials was maintained against a wide set of, but not all, assumptions about chimpanzee susceptibility to HIV.Significance to Biomedical Research: Replacing rules-of-thumb with more formal quantitative analyses has improved the effectiveness of primate usage, particularly in setting up SIV titrations in macaques. Because not all assumptions about chimpanzee susceptibility to HIV produce significance at the 0.05 level, objective assessment of HIV treatment trials in chimpanzees is problematical.